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Help with exponential function word problem

linapril

New member
Dec 21, 2012
23
The number of bacteria in a culture is given by B(t) = 40e0.6t, where t is the time in days.
How many bacteria are there after 2 days?
I substituted t = 2, and got this:

2B = 40e1.2
which I simplified to become this
B = 66.4 days

Apparently this answer is wrong though, can someone explain why?
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,851
The number of bacteria in a culture is given by B(t) = 40e0.6t, where t is the time in days.
How many bacteria are there after 2 days?
I substituted t = 2, and got this:

2B = 40e1.2
which I simplified to become this
B = 66.4 days

Apparently this answer is wrong though, can someone explain why?
Hi linapril! :)

After substitution you have B(2) = 40e1.2
The left side B(2) is not a multiplication.
B(2) is a special notation that represents the number of bacteria after 2 days.
We say that B is a function of time.

So your answer is just 40e1.2 = 132.8 days.
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
However, the answer is NOT "132.8 days" it is, rather, 132.8 bacteria.